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I started wondering what share of all world's languages are polysynthetic (on any practical definition of polysynthetic, i.e. the prototype approach, the macroparameter theory (Baker 1995), etc.), and I can't find even a rough estimate. Does anyone know?
Some other parametric values do have counts, for instance, you often learn that SOV languages constitute almost a half of world's languages. But nothing like that for isolation, agglutination and polysynthesis?
I think the problem lies in the "on any practical definition" part. After decades in the field, I still don't know what the difference between agglutinative and polysynthetic is. Imbabura Quechua is an "agglutinative" language with a small morphology, and Sanskrit is an analytic language with a big morphology. Counting morphemes doesn't help, you have to have more sophisticated metrics of "combinability" and "functional uniqueness". Even if such notions were computationally defined, processing data from languages would require a lot of work, compared to what's required to determine if the dominant word order is SOV.
I won't answer this directly but rather give resources that I think can answer it.
The WALS (World Atlas of Language Structures) has three chapters and accompanying maps on inflection types, 20, 21, and 22. They have a broad inventory of languages.
They do not use the same terminology as the classes agglutinative, isolating, etc. but do start from analytic and synthetic and refine it from there.
But from those maps you can tell frequency almost directly; they give the number of languages in their inventory with each particular feature, with all the limitations of such an inventory (selection bias, essentialism (lack of vagueness), your favorite may not be in there, etc).
You'll notice there there is no single map for SVO permutations either.
Originally polysynthesis only meant that an average word had a high content of morphems or meaning elements, without any clear definition how high it should be to call a language polysynthetic.
Later on one tends to call languages that are head marking for at least subject and object as polysynthetic, and one will often add the criterium of noun incorporation. But even if a language has these traits, it does not necessarily have a high content of elements in an average word.
I would define a polysynthetic language as one with both these traits.
Remark that a headmarking language can be dependentmarking at the same time, also called doublemarking, and of cource still be polysynthetic.
Agglutination or fusing of elements have nothing to do wuth the definition, exept that a polysynthetic language must at least be halfly agglutinating to be learnable.
It is very difficult to answar how common this language type is, because many languages have structures that are not so easily classified.
Italian, French and Spanish, for example have a higly templatic verbal group consisting of the main verb, auxiliary verbs, object clitics and adverbial clitics, and these languages are partially headmarking. And these clitics behave more like affixes than just clitics.
So these languages are at least very near to be polysynthetic, and the same holds for modern Greek.
There is also a bias against calling traditional culture languages, like Hungarian, Georgian, Romance languages and Modern Greek polysynthetid, because that would be the same as classifying them togeather with the languages of peoples tagged as primitive.
